How to Solve a Mid-Problem Calculus Step?

[ElDavidas]

Hi,

could someone please clarrify how to do this step? It's midway through a large problem and I'm not so sure about it.

y is a function of x.

$$\frac {d}{dx} ( \frac {y} \sqrt{1 + y'}} )$$

Please excuse the Latex. The square root of 1 + y' is being taken on the denominator .

Do you just use the quotient rule? and does $\frac {d} {dx}y$ equal $y'$?

thanks

 

[z-component]

I can't see the LaTeX but dy/dx does equal y'.

dy/dx is Leibniz's notation and using the prime mark is Lagrange's notation.

f(x)=y, so f'(x)=y' and if y is a function of x then the dy/dx means the derivative of y with respect to x.

 

[z-component]

Yes, use the quotient rule. To differentiate the square root expression you could use the chain rule. It may help to look at the denominator as $$(1+y')^\frac{1}{2}$$.

 

[HallsofIvy]

Further, since that is a function of y and you are differentiating with respect to x, you will have to multiply each derivative by y'.